ECO2011: Homework 10
Due on April 29, 5 pm
1. Consider the relationship between monopoly pricing and price elasticity of demand. Suppose the marginal cost is always zero.
a. Explain why a monopolist will never produce a quantity at which the demand curve is inelastic. (Hint: If demand is inelastic and the firm raises its price, what happens to the profit?) (5pt)
b. Draw a diagram for a monopolist, precisely labeling the portion of the demand curve that
is inelastic. (Hint: The answer is related to the marginal-revenue curve.) (5pt)
c. On your diagram, show the quantity and price that maximize profit. (5pt)
2. A small town is served by many competing supermarkets, which have the same constant marginal cost.
a. Using a diagram of the market for groceries, show the consumer surplus, producer surplus, and total surplus. (5pt)
b. Now suppose that the independent supermarkets combine into one chain. That is, they form. a monopoly. Suppose the marginal cost remains unchanged. Using a new diagram, show the new consumer surplus, producer surplus, and total surplus. Relative to the competitive market, what is the transfer from consumers to producers? What is the deadweight loss? (10pt)
3. Consider a monopolist who wants to maximize short-run profit. It has the following short-run total cost function:
TC = 2/1Q2
where Q is the monopoly’s quantity produced. The market demand curve for the monopoly is:
QD = 120 − P,
where P is the price and QD is the market demand of the good.
a) Calculate the marginal-revenue curve, the average-total-cost curve, the average-variable- cost curve, and the maginal-cost curve. Graph all of them in a diagram. Also graph the demand curve in the same diagram.(8pt)
b) Calculate the price charged by this monopolist. What is the quantity sold? What is the profit? Show your work. Demonstrate the profit in the diagram you drew in question a).(10pt)
c) Suppose the fixed costs change to 2500, i.e., TC = 2/1Q2 + 2500. Would the price charged by the monopolist change? Explain. What is the new profit? (Hint: Would the monopolist shut down the business?) (5pt)
d) Find the price and quantity that would maximize social welfare. Show your work. (6pt)
e) Calculate the deadweight loss from monopoly. (6pt)
f) Suppose the government levies a per unit tax of 30 on the monopolist. Find the price and quantity that maximize the monopolist’s profit. Calculate CS , PS , TR (tax revenue), TS , and DWL. (15pt)